Fluorescence intensity correcting method, fluorescence intensity calculating method, and fluorescence intensity calculating apparatus

ABSTRACT

A fluorescence intensity calculating apparatus, includes a measuring section configured to receive fluorescences generated from plural fluorescent dyes excited by radiating a light to a microparticle multiply-labeled with the plural fluorescent dyes having fluorescence wavelength bands overlapping one another by photodetectors which correspond to different received light wavelength bands, respectively, and whose number is larger than the number of fluorescent dyes, and obtain measured spectra by collecting detected values from the photodetectors, and a calculating section configured to approximate the measured spectra based on a linear sum of single-dyeing spectra obtained from the microparticle individually labeled with the fluorescent dyes, thereby calculating intensities of the fluorescences generated from the fluorescent dyes, respectively.

CROSS REFERENCES TO RELATED APPLICATIONS

The present application is a continuation of U.S. application Ser. No.16/848,115, filed Apr. 14, 2020, which is a continuation of U.S.application Ser. No. 16/295,519, filed Mar. 7, 2019, which is acontinuation of U.S. application Ser. No. 14/452,085, filed Aug. 5,2014, which is a continuation of U.S. application Ser. No. 13/089,961,filed Apr. 19, 2011, which claims priority to Japanese Priority PatentApplication JP 2010-104566 filed in the Japan Patent Office on Apr. 28,2010, the entire content of each of which is hereby incorporated byreference herein.

BACKGROUND

The present application relates to a fluorescence intensity correctingmethod, a fluorescence intensity calculating method, and a fluorescenceintensity calculating apparatus. More specifically, the applicationrelates to a fluorescence intensity correcting method, a fluorescenceintensity calculating method, and a fluorescence intensity calculatingapparatus each of which is capable of precisely calculating intensitiesof fluorescences generated from plural fluorescent dyes, respectively,with which a microparticle is multiply-labeled.

Heretofore, there has been used an apparatus (such as a flow cytometer)for labeling a microparticle such as a cell with a fluorescent dye, andmeasuring an intensity or a pattern of a fluorescence generated from thefluorescent dye excited by radiating a laser beam to the microparticle,thereby measuring characteristics of the microparticle. In recent years,a multicolor measurement has been carried out in order to more minutelyanalyze the characteristics of the cell or the like. In this case, themulticolor measurement is such that a microparticle is labeled withplural fluorescent dyes, and lights generated from the respectivefluorescent dyes are measured by using plural photodetectors (such asPMTs) corresponding to different received light wavelength bands,respectively. In the multicolor measurement, the fluorescent dyesagreeing in fluorescence wavelength with the received light wavelengthbands of the respective photodetectors are selected and used.

On the other hand, fluorescence central wavelengths of the fluorescentdyes (such as FITC, phycoerythrin (PE) and allophycocyanin (APC)) areclose to one another. Thus, the wavelength band exists in which thefluorescence spectra overlap one another. Therefore, in the case wherethe multicolor measurement is carried out based on a combination ofthese fluorescent dyes, even when the fluorescences generated from therespective fluorescent dyes are separated from one another by thewavelength band by using an optical filter, the fluorescence generatedfrom the fluorescent dye other than objective fluorescent dyes is leakedto the photodetectors in some cases. When the leakage of thefluorescence occurs, the fluorescence intensities measured by therespective photodetectors become larger than the true intensities of thefluorescences generated from the objective fluorescent dyes, and thusmismatch occurs in data.

Fluorescence correction (compensation) for subtracting the fluorescenceintensity for the leakage from the fluorescence intensity measured bythe photodetector is carried out in order to correct the mismatch in thedata. The fluorescence correction is such that an electrical ormathematical correction is added to a pulse on a dedicated circuit sothat the fluorescence intensity measured by the photodetector becomesthe true intensity of the fluorescence generated from the objectivefluorescent dye.

A method of expressing the fluorescence intensities measured by therespective photodetectors in the form of a vector, and causing aninversion matrix of a leakage matrix previously set to act on thevector, thereby calculating a true intensity of a fluorescence generatedfrom an objective fluorescent dye is known as a method of mathematicallycarrying out the fluorescence correction. This method is described inJapanese Patent Laid-Open No. 2003-83894 (refer to FIGS. 10 and 11). Theleakage matrix is created by analyzing the fluorescence wavelengthdistribution of the microparticle single-labeled with fluorescent dye,and the fluorescence wavelength distribution of the fluorescent dyes isarranged in the form of a column vector. In addition, an inversionmatrix of the leakage matrix is referred to as “a correction matrix” aswell.

SUMMARY

Since with the fluorescence intensity correcting method using thecorrection matrix, the inversion matrix of the leakage matrix is causedto act on the vector having the fluorescence intensities measured by therespective photodetectors as elements thereof, it is necessary that theleakage matrix is a square matrix.

A matrix size of the leakage matrix depends on the number of fluorescentdyes used and the number of photodetectors used. Therefore, in orderthat the correction matrix may be the square matrix, it is necessarythat the number of fluorescent dyes used and the number ofphotodetectors used are equal to each other. FIGS. 10A to 10C and 11exemplify the case where five color measurements are carried out byusing five kinds of fluorescent dyes (FITC, PE, ECD, PC5, and PC7), andfive photodetectors.

Recently, for the purpose of meeting user's need that the number ofusable fluorescent dyes is desired to be increased in order to minutelyanalyze the characteristics of the cell or the like, an apparatus inwhich the number of photodetectors is increased has also been developed.In such an apparatus that a large number of photodetectors is disposed,the number of photodetectors used in the measurement may be larger thanthe number of fluorescent dyes used in the labeling for themicroparticle in some cases. In such cases, for the purpose ofeffectively apply the fluorescence correction using the correctionmatrix, it is necessary that the number of fluorescent dyes used and thenumber of photodetectors used are equal to each other. Therefore, themeasured data is utilized by suitably selecting the photodetectors whosenumber agrees with the number of fluorescent dyes without using themeasured data obtained from all the photodetectors. For this reason,there is caused a problem that the resulting measured data is noteffectively utilized.

The present application has been made in order to solve the problemsdescribed above, and it is therefore desirable to provide a fluorescenceintensity correcting method, a fluorescence intensity calculatingmethod, and a fluorescence intensity calculating apparatus each of whichis capable of effectively utilizing measured data obtained from allphotodetectors without depending on the number of fluorescent dyes inthe case where a microparticle labeled with plural fluorescent dyes ismulticolor-measured by plural photodetectors, thereby preciselycalculating intensities of fluorescences generated from respectivefluorescent dyes.

In order to attain the desire described above, according to anembodiment, there is provided a fluorescence intensity correcting methodincluding the steps of: receiving fluorescences generated from pluralfluorescent dyes excited by radiating a light to a microparticlemultiply-labeled with the plural fluorescent dyes having fluorescencewavelength bands overlapping one another by photodetectors whichcorrespond to different received light wavelength bands, respectively,and whose number is larger than the number of fluorescent dyes; andapproximating measured spectra obtained by collecting detected valuesfrom the plural photodetectors based on a linear sum of single-dyeingspectra obtained from a microparticle individually labeled with thefluorescent dyes.

In the fluorescence intensity correcting method described above, theapproximation of the measured spectra based on the linear sum of thesingle-dyeing spectra can be carried out by using a least-squaresmethod. In addition, at this time, when an invalid value(s) is(are)contained in the detected values, the invalid detected value(s) may beexcluded, and thus measured spectra may be approximated based on thelinear sum of the single-dyeing spectra. By excluding the invaliddetected value(s), a correction precision of the fluorescence intensityis enhanced.

Specifically, in the fluorescence intensity correcting method describedabove, a parameter ak (k=1 to m) at which an evaluation functionexpressed by following Expression gets a minimum value is obtained byusing a normal equation or singular value decomposition, thereby makingit possible to calculate intensities of the fluorescences generated fromthe fluorescent dyes, respectively:

$\chi^{2} \equiv {\sum\limits_{i = 1}^{N}\left\lbrack \frac{y_{i} - {\sum\limits_{k = 1}^{M}{a_{k}{X_{k}\left( x_{i} \right)}}}}{\sigma_{i}} \right\rbrack^{2}}$

where X_(k)(x_(i)) represents a detected value from the i-thphotodetector in the single-dyeing spectrum of the k-th fluorescent dye,y_(i) represents a detected value from the i-th photodetector in themeasured spectra, and σ_(i) represents a reciprocal number of a weightfor the measured value from the i-th photodetector. In this case, thereciprocal number of the weight, for example, may be a measurement errorvariance of the i-th photodetector, or the like. If there is noreciprocal number of the weight, all σ_(i) may be set as 1.

In addition, when the invalid value(s) is(are) contained in the detectedvalues, in the fluorescence intensity correcting method described above,the parameter a_(k) (k=1 to m) at which the evaluation functionexpressed by following Expressions gets the minimum value is obtained,thereby making it possible to calculate the intensities of thefluorescences generated from the respective fluorescent dyes:

${\chi^{2} \equiv {\sum\limits_{i = 1}^{N}\left\lbrack \frac{y_{i} - {\sum\limits_{k = 1}^{M}{a_{k}{X_{k}\left( x_{i} \right)}}}}{\sigma_{i}} \right\rbrack^{2}}}{or}{{X_{k}^{\prime}\left( x_{i} \right)} = {{X_{i}\left( x_{i} \right)}\left( {{k = {1 \sim M}},{i = {1 \sim N_{1}}}} \right)}}{{X_{k}^{\prime}\left( x_{i} \right)} = {0\left( {{k = {1 \sim M}},{i = {{N_{1} + 1} \sim N}}} \right)}}{\chi^{2} \equiv {\sum\limits_{i = 1}^{N}\left\lbrack \frac{y_{i} - {\sum\limits_{k = 1}^{M}{a_{k}{X_{k}^{\prime}\left( x_{i} \right)}}}}{\sigma_{i}} \right\rbrack^{2}}}$

where X_(k)(x_(i)) represents a detected value from the i-thphotodetector in the single-dyeing spectrum of the k-th fluorescent dye,y_(i) represents a detected value from the i-th photodetector in themeasured spectra, and σ_(i) represents a reciprocal number of a weightfor the measured value from the i-th photodetector. However, an invaliddetected value is taken to be y_(i) (i=“N₁+1” to N), and a validdetected value is taken to be y_(i) (i=1 to N₁).

According to another embodiment, there is provided a fluorescenceintensity calculating method including the steps of: receivingfluorescences generated from plural fluorescent dyes excited byradiating a light to a microparticle multiply-labeled with the pluralfluorescent dyes having fluorescence wavelength bands overlapping oneanother by photodetectors which correspond to different received lightwavelength bands, respectively, and whose number is larger than thenumber of fluorescent dyes, and obtaining measured spectra by collectingdetected values from the photodetectors; and approximating the measuredspectra based on a linear sum of single-dyeing spectra obtained from themicroparticle individually labeled with the fluorescent dyes, therebycalculating intensities of the fluorescences generated from thefluorescent dyes, respectively.

According to still another embodiment, there is provided a fluorescenceintensity calculating apparatus including: a measuring section forreceiving fluorescences generated from plural fluorescent dyes excitedby radiating a light to a microparticle multiply-labeled with the pluralfluorescent dyes having fluorescence wavelength bands overlapping oneanother by photodetectors which correspond to different received lightwavelength bands, respectively, and whose number is larger than thenumber of fluorescent dyes, and obtaining measured spectra by collectingdetected values from the photodetectors; and a calculating section forapproximating the measured spectra based on a linear sum ofsingle-dyeing spectra obtained from the microparticle individuallylabeled with the fluorescent dyes, thereby calculating intensities ofthe fluorescences generated from the fluorescent dyes, respectively.

In the present embodiment, biologically-relevant microparticles such asa cell, a microbe, and a liposome, synthetic particles such as a latexparticle, a gel particle, and an industrial particle, and the like aregenerally contained in “the microparticles.”

A chromosome, a liposome, a mitchondrion, an organelle (cell organelle),and the like composing various kinds of cells are contained in thebiologically-relevant microparticles. An animal cell (such as atrilineage cell) and a plant cell are contained in the cells. A bacilloclass such as a Bacillus coli, a virus class such as a tabacco mosaicvirus, a fungus class such as a yeast fungus, and the like are containedin the microbes. In addition, a biologically-relevant polymer such as anucleic acid, a protein, and a complex thereof may also be contained inthe biologically-relevant microparticles. In addition, the industrialparticle, for example, may also be an organic or inorganic polymermaterial, a metal or the like. Polystyrene, styrene, divinylbenzene,polymethyl methacrylate, or the like is contained in the organic polymermaterial. A glass, silica, a magnetic material or the like is containedin the inorganic polymer material. Also, gold colloid, aluminum or thelike is contained in the metal. Although it is not out of the way that ashape of each of those microparticles is generally a spherical shape,the shape thereof may also be nonspherical shape, and a size, a mass andthe like thereof are especially by no means limited.

In addition, in the present embodiment, “the invalid detected value”means a detected value having the obviously low reliability, and also adetected value having the possibility that when the detected value isused in the calculation, the precision of calculating the fluorescenceintensity is reduced. For example, the detected value obtained in thephotodetector corresponding to the wavelength out of the fluorescencewavelength band of a certain fluorescent dye as the received lightwavelength band when the measurement about the microparticlesingle-labeled with the certain fluorescent dye is carried out, thedetected value obtained in the photodetector when the measurement iscarried out by radiating the light having the wavelength band out of theexcited wavelength band to the microparticle single-labeled with acertain fluorescent dye, and the like are contained in the invaliddetected value. These detected values ought not to be detected intheory. However, in the actual apparatus, from the reason that thefluorescence which should be mechanically shielded is leaked, theelectrical noise is applied and so forth, these detected values areobtained in some cases. In addition, the characteristics of the specificphotodetector become worse from some sort of reason, and as a result,such low reliable detected values are obtained in some cases.

As set forth hereinabove, according to the present embodiment, it ispossible to provide the fluorescence intensity correcting method, thefluorescence intensity calculating method, and the fluorescenceintensity calculating apparatus each of which is capable of effectivelyutilizing the measured data obtained from all the photodetectors withoutdepending on the number of fluorescent dyes in the case where themicroparticle labeled with the plural fluorescent dyes ismulticolor-measured by the plural photodetectors, thereby preciselycalculating the intensities of the fluorescences generated from therespective fluorescent dyes.

Additional features and advantages are described herein, and will beapparent from the following Detailed Description and the figures.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 is a graphical representation explaining an approximated curvesobtained by approximating measured spectra based on a linear sum ofsingle-dyeing spectra;

FIG. 2 is a diagram explaining elements of a matrix of (N×M);

FIGS. 3A to 3D are a plot diagram before fluorescence correction inPE-PE-TR two-dimensional plotting in positive process control, a plotdiagram obtained by executing fluorescence correction processing byusing an inversion matrix method as an existing technique in thePE-PE-TR two-dimensional plotting in positive process control, a plotdiagram obtained by executing fluorescence correction processing byusing a least-squares method (normal equation) in the PE-PE-TRtwo-dimensional plotting in positive process control, and a plot diagramobtained by executing fluorescence correction processing by executing aleast-squares method (SVD method) in the PE-PE-TR two-dimensionalplotting in positive process control, respectively;

FIG. 4 is a diagram explaining definition of an index in accordance withwhich right and wrong of separation between cell groups are evaluated;

FIGS. 5A to 5K are plot diagrams each obtained by subjecting simulationdata to the fluorescence correction processing by using the inversionmatrix method as the existing method, respectively;

FIGS. 6A to 6K are plot diagrams each obtained by subjecting simulationdata to fluorescence correction processing by using a least-squaresmethod in the present embodiment, respectively;

FIG. 7 is a spectrogram showing an example of measured spectra in whichinvalid detected values are contained, respectively;

FIG. 8 is a spectrogram showing spectra obtained by excluding theinvalid detected values from the measured spectra shown in FIG. 7;

FIGS. 9A-9G are diagrams showing results obtained by subjecting thespectra shown in FIGS. 7 and 8 to the fluorescence correcting processingby using a method utilizing a least-squares method in the presentembodiment, thereby comparing right and wrong of separation with eachother;

FIGS. 10A to 10C are diagrams explaining a fluorescence correctingmethod using an existing correction matrix; and

FIG. 11 is a diagram explaining matrix elements of the existingcorrection matrix.

DETAILED DESCRIPTION

Embodiments of the present application will be described below in detailwith reference to the drawings.

The preferred embodiments of the present application will be describedin detail hereinafter with reference to the accompanying drawings. It isnoted that embodiments of the present application which will bedescribed below merely exemplifies typical embodiments of the presentapplication, and thus the scope of the present application is notintended to be construed in a limiting sense by the embodiments. It isalso noted that the description will be given below in accordance withthe following order.

1. Fluorescence Intensity Correcting Method

(1-1) Approximated Curves

(1-2) Linear Least-Squares Equation

(1-2-1) Normal Equation

(1-2-2) Singular Value Decomposition

2. Fluorescence Intensity Calculating Method

(2-1) Labeling

(2-2) Measurement

(2-3) Fluorescence Intensity Calculation

3. Fluorescence Intensity Calculating Apparatus

1. Fluorescence Intensity Correcting Method

(1-1) Approximated Curves

The feature of the fluorescence intensity correcting method according toa first embodiment is that measured spectra are approximated based on alinear sum of single-dyeing spectra, thereby calculating trueintensities of fluorescences generated from respective fluorescent dyes.“The measured spectra” are obtained by receiving fluorescences generatedfrom fluorescent dyes excited by radiating a light to a microparticlemultiply-labeled with plural fluorescent dyes having fluorescencewavelength bands overlapping one another by photodetectors whichcorrespond to different received light wavelength bands and which numberis larger than the number of fluorescent dyes, and collecting detectedvalues from the respective photodetectors. In addition, “thesingle-dyeing spectra” are fluorescence wavelength distributions of therespective fluorescent dyes, and are obtained by receiving fluorescencesgenerated from fluorescent dyes excited by radiating a light to amicroparticle individually labeled with fluorescent dyes byphotodetectors, respectively, and by collecting detected values from therespective photodetectors.

An approximated curve which is obtained by approximating measuredspectra based on a linear sum of single-dyeing spectra will now bedescribed with reference to FIG. 1.

In FIG. 1, an X-axis represents an observation point, and a Y-axisrepresents a detected value. In FIG. 1, a detected value of afluorescence received by a photodetector x₁ is indicated by y₁, adetected value of a fluorescence received by a photodetector x₂ isindicated by y₂, and a detected value of a fluorescence received by aphotodetector x_(n) is indicated by y_(n). A line connecting thedetected values y₁ to y_(n) is a measured spectrum.

In addition, in FIG. 1, a curve (basis function) representing asingle-dyeing spectrum of a first fluorescent dye (fluorescent dye 1) isindicated by X₁(x), a curve representing a single-dyeing spectrum of asecond fluorescent dye (fluorescent dye 2) is indicated by X₂(x), and acurve representing a single dyeing spectrum of an m-th fluorescent dye(fluorescent dye m) is indicated by X_(m)(x).

With the photodetectors, the fluorescences from all the fluorescent dyesof the fluorescent dye 1 to the fluorescent dye m are received in astate in which those fluorescences are leaked at predetermined rates,respectively. For this reason, the detected values obtained from therespective photodetectors can be approximated as a sum of valuesobtained by multiplying basis functions of the fluorescent dye 1 to thefluorescent dye m by the respective predetermined rates in accordancewith Expression (4):

$\begin{matrix}{{y(x)} = {\sum\limits_{k = 1}^{M}{a_{k} \cdot {X_{k}(x)}}}} & (4)\end{matrix}$

where a_(k) represents the rate of the leakage of the fluorescence fromthe fluorescent dye k to the photodetector x_(k). Here, the rate a_(k)of the leakage of the fluorescence from the fluorescent dye k to thephotodetector x_(k) is regulated by the fluorescence intensity (truefluorescence intensity) of the fluorescent dye k.

Specifically, for example, the detected value y₁ obtained from thephotodetector x₁ is approximated as a sum y(x₁) of a value obtained bymultiplying the basis function X₁(x₁) of the fluorescent dye 1 by therate a₁ to a value obtained by multiplying the basis function X_(m)(x₁)of the fluorescent dye m by the rate a_(m). Also, the leakage ratesa_(k) (k=1 to m) of the fluorescences of the fluorescent dyes 1 to m tothe photodetector x₁ correspond to the fluorescence intensities of thefluorescent dyes 1 to m, respectively.

An approximated curve represented by Expression (4) is obtained byobtaining the leakage rate a_(k) by using a linear least-squares methodwhich will next be described. The leakage rate a_(k) is equal to thetrue fluorescence intensity of the corresponding one of the fluorescentdyes.

(1-2) Linear Least-Squares Method

For obtaining a_(k), firstly, an evaluation function (chi-square)expressed by Expression (5) is defined. Also, such a parameter a_(k)(k=1 to m) at which Expression (5) gets a minimum value is obtained.

$\begin{matrix}{\chi^{2} \equiv {\sum\limits_{i = 1}^{N}\left\lbrack \frac{y_{i} - {\sum\limits_{k = 1}^{M}{a_{k}{X_{k}\left( x_{i} \right)}}}}{\sigma_{i}} \right\rbrack^{2}}} & (5)\end{matrix}$

where σ₁ represents a reciprocal number of a weight for the measuredvalue from the i-th photodetector. In this case, the reciprocal numberof the weight, for example, may be a measurement error variance of thei-th photodetector. If there is no reciprocal number of the weight, allσ_(i) may be set as 1.

(1-2-1) Normal Equation

Next, a matrix A of (N×M) (refer to FIG. 2) composed of elementsexpressed by Expression (6), and a vector b having a length N(Expression (7)) are both defined, and a vector in which M parameters a₁to a_(m) obtained from application is set as a.

$\begin{matrix}{A_{ij} = \frac{X_{j}\left( x_{i} \right)}{\sigma_{i}}} & (6) \\{b_{i} = \frac{y_{i}}{\sigma_{i}}} & (7)\end{matrix}$

Expression (5) gets a minimum value when all values obtained bydifferentiating χ² by M parameters a_(k) become zero.

$\begin{matrix}{{0 = {{\sum\limits_{i = 1}^{N}{{{\frac{1}{\sigma_{j}^{2}}\left\lbrack {y_{i} - {\sum\limits_{j = 1}^{M}{a_{j}{X_{j}\left( x_{i} \right)}}}} \right\rbrack} \cdot {X_{i}\left( x_{i} \right)}}k}} = 1}},\cdots,M} & (8)\end{matrix}$

When the order for obtaining the sum is changed, Expression (8) can betransformed into Expression (9) as a matrix equation (normal equation):

$\begin{matrix}{{\sum\limits_{j = 1}^{M}{a_{kj}a_{j}}} = \beta_{k}} & (9)\end{matrix}$

where [a_(kj)] represents a matrix of (M×N), and [β_(k)] represents avector having a length M.

$\begin{matrix}{{a_{kj} = {\sum\limits_{i = 1}^{N}{\frac{{X_{j}\left( x_{j} \right)} \cdot {X_{k}\left( x_{i} \right)}}{\sigma_{j}^{2}}{that}{is}}}},{\lbrack\alpha\rbrack = {A^{T} \cdot A}}} & (10) \\{{\beta_{k} = {\sum\limits_{i = 1}^{N}{\frac{y_{i} \cdot {X_{k}\left( x_{j} \right)}}{\sigma_{i}^{2}}{that}{is}}}},{\lbrack\beta\rbrack = {A^{T} \cdot b}}} & (11)\end{matrix}$

Therefore, when Expression (8) described above is expressed in the formof a matrix, Expression (12) is obtained as follows.

[α]·a=[β] or (A ^(T) ·A)−a=A ^(T) ·b  (12)

Expression (12) is a simultaneous linear equation with M unknowns, andthus a_(j) is obtained by solving Expression (12).

(1-2-2) Singular Value Decomposition

Instead of utilizing the method using the normal equation describedabove, a vector in which a₁ to a_(m) as M parameters may also beobtained by utilizing singular value decomposition.

The singular value decomposition (SVD) is based on the theorem of alinear algebra in which an arbitrary matrix A of (N×M) is written in theform of the product of three matrices of U, W and V^(T) (refer toExpression (13)). The matrix U is a column orthogonal matrix of (N×M),the matrix W is a diagonal matrix of (M×M) (a diagonal component w_(i)is non-negative and is a referred to as a singular value), the matrixV^(T) is a transposition of an orthogonal matrix V of (M×M). Inaddition, the matrices U and V are the orthonormal matrices. In thiscase, the columns are orthonormal to one another (refer to Expression(14)).

$\begin{matrix}{(A) = {{UWV}^{T} = {(U) \cdot \begin{pmatrix}w_{1} & & & & \\ & w_{2} & & 0 & \\ & & \ddots & & \\ & 0 & & \ddots & \\ & & & & w_{m}\end{pmatrix} \cdot \left( V^{x} \right)}}} & (13) \\{{\left( U^{T} \right) \cdot (U)} = {{\left( V^{T} \right) \cdot (V)} = (1)}} & (14)\end{matrix}$

Expression (5) described above can be rewritten as Expression (15):

χ² =|A·a−b| ²  (15)

When the matrix A is subjected to the singular value decomposition toobtain the matrices U, W and V as with Expression (13) described above,the vector, a, which minimizes Expression (15) is obtained fromExpression (16). This operation is called backward substitution. Ifthere is a sufficiently small value in w_(i), 1/w_(i) is replaced with 0and the processing is advanced.

a=V·[diag(1/w _(i))]·(U ^(T) ·b)  (16)

2. Fluorescence Intensity Calculating Method

Next, a description will be given with respect to a fluorescenceintensity calculating method according to a second embodiment to whichthe fluorescence intensity correcting method of the first embodimentdescribed above is applied.

(2-1) Labeling

Firstly, the microparticle as an object of the measurement is labeledwith plural fluorescent dyes. The labeling of the fluorescent dye isgenerally carried out by coupling a fluorescent-labeled antibody to amolecule(s) existing on a surface of a microparticle. Although thefluorescent dye is especially by no means limited, for example, thereare given phycoerythlin (PE), FITC, PE-Cy5, PE-Cy7, PE-Texas red,allophycocyanin (APC), APC-Cy7, ethidium bromide, propidium iodide,hoechst 33258/33342, DAPI, acridine orange, chromomycin, mithramycin,olivomycin, pyronin Y, thiazole orange, rhodamine 101 isothiocyanate,BCECF, BCECF-AM, C.SNARF-1, C.SNARF-1-AMA, aequorin, Indo-1, Indo-1-AM,Fluo-3, Fluo-3-AM, Fura-2, Fura-2-AM, oxonole, Texas red, rhodamine 123,10-N-nonyl-acridine orange, fluorecein, fluorescein diacetate,carboxyfluorescein, caboxyfluorescein diacetate,carboxydichlorofluorescein, carboxydichlorofluorescein diacetate, andthe like.

(2-2) Measurement

The microparticle labeled with the fluorescent dyes is measured by usinga multicolor measuring apparatus in which photodetectors whichcorrespond to different received light wavelength bands and whose numberis larger than the number of fluorescent dyes are disposed. Also, thedetected values obtained from the respective photodetectors arecollected to obtain the measured spectra. The movement manipulation canbe carried out similarly to the case of the method which is normallycarried out.

(2-3) Fluorescence Intensity Calculation

The measured spectra are approximated based on the linear sum of thesingle-dyeing spectra in accordance with the method described above,thereby calculating the true fluorescence intensities generated from therespective fluorescent dyes. At this time, when the measurement errorvariance in the photodetector is not clear, all σi in Expression (5) maybe set as 1. The single-dyeing spectra may be obtained by preparing thesample individually labeled with the fluorescent dyes whenever themeasurement is carried out, or the standard spectra whose data ispreviously stored may be utilized.

3. Fluorescence Intensity Calculating Apparatus

The fluorescence intensity calculating apparatus according to a thirdembodiment is composed of a fluid system, an optical system, a sortingsystem, a data processing system, and the like similarly to the case ofthe existing flow cytometer or the like.

The fluid system is a section for causing a sample liquid containingtherein microparticles as an object of a measurement to flow to a centerof a laminar flow of a sheath liquid in a flow cell, thereby arrangingthe microparticles in a line within the flow cell. Instead of using theflow cell, the microparticles may be arranged in a line within a flowpath formed on a microchip.

The optical system is a measuring section for receiving fluorescencesgenerated from fluorescent dyes excited by radiating a light to amicroparticle labeled with the fluorescent dyes by photodetectors, andcollecting detected values from the respective photodetectors, therebyobtaining measured spectra. With the optical system, a scattered lightsuch as a forward scattered light, a side scattered light, a Rayleighscattered light, or a Mie scattered light is also detected.Specifically, the optical system is composed of a laser light source, aradiating system and a detecting system. In this case, the radiatingsystem is composed of a condensing lens and a dichroic mirror forcondensing and radiating a laser beam to the microparticle, a band-passfilter, and the like. Also, the detecting system detects thefluorescence and the scattered light generated from the micropaticle byradiating the laser beam to the micropaticle. The detecting system, forexample, is composed of a photo multiplier tube (PMT), an area imagepickup element such as a CCD or a CMOS element, and the like. Also, thephotodetectors corresponding to different received light wavelengthbands, respectively, are disposed in the detecting system.

When the microparticles are intended to be sorted, a sample liquid isejected as droplets containing therein the respective microparticles toa space in the outside of the flow cell, and a movement directions ofthe droplets are controlled, thereby sorting the microparticle havingdesired characteristics. The sorting system is composed of a vibratingelement such as a piezo element, a charging section, paired electrodes,and the like. In this case, the vibrating element changes the sampleliquid into the droplets and discharges the droplets from the flow cell.The charging section charges the droplets ejected with the electriccharges. Also, the paired electrodes are disposed to face each otheralong the movement directions of the droplets through the movingdroplets.

The detected values are input as electrical signals from thephotodetectors to the data processing system. The data processing systemanalyzes the optical characteristics of the microparticles based on theelectrical signals. Also, the data processing system approximates themeasured spectra obtained by collecting the detected values from therespective photodetectors based on the linear sum of the single-dyeingspectra in accordance with the method described above, therebycalculating the true fluorescence intensities generated from therespective fluorescent dyes. For this reason, the data processing systemhas a recording medium, such as a hard disc, for storing therein aprogram for executing the steps of the fluorescence intensitycalculating method described above according to the second embodiment, aCPU for executing the program, a memory, and the like.

EXAMPLE 1

Measured data obtained from the analysis using positive process control(whole blood control specimen) (Immuno-Trol, Beckman-Coulter, Inc.) fora commercially available flow cytometry was processed by the existingfluorescence correcting method using an inversion matrix, and thefluorescence correcting method according to the first embodiment. Also,the processing results were compared and examined.

The labeling for Immuno-Trol was carried out by using four kinds offluorescence reagents of FITC, PE, PE-TR, and PE-Cy5 in accordance withan accompanying appended document. FIGS. 3A to 3D are PE-PE-TRtwo-dimensional plot diagrams obtained when the gate is applied to acell group which seems likely to be lymphocytes in an FITC-SSCtwo-dimensional plot diagram, respectively.

FIG. 3A is a two-dimensional plot diagram when PMT (CH15) having a peakwhen the PE single-dyeing spectrum is measured is plotted on an axis ofabscissa, and PMT (CH19) having a peak when the PE-TR single-dyeingspectrum is measured is plotted on an axis of ordinate. Also, FIG. 3Acorresponds to a plot diagram before the fluorescence correction iscarried out.

FIG. 3B is a plot diagram obtained by executing fluorescence correctingprocessing by using an inversion matrix method as the existingtechnique. FIG. 3C is a plot diagram obtained by executing thefluorescence correcting processing by using a least-squares method(normal equation). Also, FIG. 3D is a plot diagram obtained by executingthe fluorescence correcting processing by using the least-squares method(SVD method).

In each of the plot diagrams shown in FIGS. 3A to 3D, respectively, anindex in accordance with which right and wrong of the separation betweenthe cell groups were evaluated was defined as follows. That is to say,in each of the plot diagrams, Log (logarithms) was taken, and centralcoordinates and a standard deviation were obtained with respect to thePE positive cell group and the PE-TR positive cell group. Also, a mutualcenter-to-center distance was taken to be D, and the two standarddeviations were taken to be σ1 and σ2, respectively (refer to FIG. 4).Also, a math formula of (D−σ1−σ2)/D″ was made an index representing theseparation between the cell groups. This index means that as a value ofthe index is larger, the separation between the cell groups is good andthe performance of the fluorescence correcting processing is favorable.

The indices in the PE-TR-PE two-dimensional plot diagram, the PE-Cy5-PEtwo-dimensional plot diagram, and the PE-Cy5-PE-TR two-dimensional plotdiagram shown in FIGS. 3A to 3D are summarized in “TABLE 1”.

TABLE 1 two-dimensional least-squares plot diagram inversion method(normal (axis of ordinate/ matrix equation·SVD axis of abscissa) methodmethod) PE-TR/PE 0.59 0.64 PE-Cy5/PE 0.61 0.65 PE-Cy5/PE-TR 0.31 0.76

In all the two-dimensional plot diagrams, the index has a larger valuein the plot diagram obtained by executing the fluorescence correctingprocessing based on the least-squares method (the normal equation or theSVD method) than in the plot diagram obtained by executing thefluorescence correcting processing based on the inversion matrix method.As a result, it is possible to confirm that the fluorescence correctingmethod according to the first embodiment provides the favorableseparation between the cell groups.

In addition, FIGS. 5A to 5K, and FIGS. 6A to 6K show two-dimensionalplot diagrams, respectively, obtained by processing simulation databased on which a spectrum waveform containing therein a noise isgenerated at random on the assumption that twelve kinds of fluorescencereagents of FITC, Alexa 500, Alexa 514, Alexa 532, PE, PE-TR, PI, Alexa600, PE-Cy5, PerCP, PerCP-Cy5.5, and PE-Cy7 are used. In FIGS. 5A to 5K,and FIGS. 6A to 6K, all FITCs are plotted on the axis of abscissa, andthe fluorescent dye written on an upper side of each of the graphs isplotted on the axis of ordinate. In the case of the graph show in FIG.4, the fluorescence correction is carried out by using the methodutilizing the inversion matrix method as the existing method. Also, inthe case of the graphs shown in FIGS. 5A to 5K, the fluorescencecorrection is carried out by using the method utilizing theleast-squares method in the present embodiment. It is understood thatalthough there are some plots which cannot be separated in the case ofthe inversion matrix method, all the plots can be satisfactorilyseparated in the case of the present embodiment.

EXAMPLE 2

The measured data in which the invalid value(s) is(are) contained, andthe measured data in which the invalid detected value(s) is(are)excluded were processed by using the fluorescence intensity correctingmethod utilizing the least-squares method. Also, the processing resultswere compared and examined.

FIG. 7 shows an example of the measured spectra in each of which theinvalid detected value(s) is(are) contained.

Graphs shown in FIG. 7 are obtained by measuring seven kinds ofsingle-dyeing spectra about AF488, PE, PerCP-Cy5.5, PE-Cy7, PI, APC, andAPC-Cy7. In this case, the seven kinds of single-dyeing spectra are allnormalized so that each of their peaks becomes 1. In FIG. 7, the axis ofabscissa represents PMT, and the axis of ordinate represents thedetected value. Also, the detected values of the fluorescence spectrumobtained by excitation made by radiation of a 488 nm-laser beam areindicated in 488Ch1 to 488Ch32, and the detected values of thefluorescence spectrum obtained by excitation made by radiation of a 640nm-laser beam are indicated in 640Ch1 to 640Ch32.

Although with regard to the fluorescent dye excited by radiation of the640 nm-laser beam, there are PerCP-Cy5.5, PE-Cy7, APC, and APC-Cy7, itis known that any of those fluorescent dyes does not generate thefluorescence with the wavelengths sensed by the detectors 640Ch1 to640Ch20 in theory. In addition, any of AF488, PE and PI is not excitedat all by radiation of the 640 nm-laser beam. Therefore, the wavelengthsappearing in 640Ch1 to 640Ch20 are the noises and thus are the invaliddetected values. FIG. 8 shows spectra in each of which these invaliddetected values are excluded.

FIGS. 9A-9G are diagrams showing results obtained by processing thespectra shown in FIGS. 7 and 8 by using the fluorescence intensitycorrecting method utilizing the least-squares method, thereby comparingright and wrong of the separation. In FIGS. 9A-9G, “All Channel”represents the results obtained by processing the measured data in whichthe invalid detected values are contained. Also, “Cut Ch1-20” representsthe results obtained by processing the data from which the invaliddetected values are excluded. It is understood that the detected values,indicated by 640Ch1 to 640Ch20, as the invalid detected values areexcluded from the measured data, whereby in particular, the separationof APC-Cy7 becomes good.

According to the fluorescence intensity correcting method, thefluorescence intensity calculating method, and the fluorescenceintensity calculating apparatus of the present embodiment, when themicroparticle labeled with the plural fluorescent dyes ismulticolor-measured by using the plural photodetectors, the measureddata obtained from all the photodetectors is effectively utilizedwithout depending on the number of fluorescent dyes, thereby making itpossible to precisely calculate the fluorescence intensities from therespective fluorescent dyes. Therefore, the fluorescence intensitycorrecting method, the fluorescence intensity calculating method, andthe fluorescence intensity calculating apparatus of the presentembodiment can contribute to that the characteristics of themicroparticle such as cell are more minutely analyzed.

It should be understood that various changes and modifications to thepresently preferred embodiments described herein will be apparent tothose skilled in the art. Such changes and modifications can be madewithout departing from the spirit and scope and without diminishing itsintended advantages. It is therefore intended that such changes andmodifications be covered by the appended claims.

The application is claimed as follows:
 1. A flow cytometer systemcomprising: a plurality of detectors configured to receive a light fromeach of microparticles labeled with a plurality of fluorescent dyes, andthe detectors corresponding to different received light wavelengthbands; and a processor circuitry configured to calculate fluorescenceintensity for each of the fluorescent dyes using a linear sum ofsingle-dyeing spectra, wherein a number of single-dyeing spectra beingequal or less than a number of the detectors, and output a plot diagramof the calculated fluorescence intensity.
 2. The flow cytometer systemaccording to claim 1, further comprising: a sorting device configured tosort a microparticle having desired characteristics in themicroparticles.
 3. The flow cytometer system according to claim 2,wherein the sorting device comprises a vibrating element configured tovibrate sample liquid including the microparticles; a charging sectionconfigured to charge a droplet generated by the vibrating element withelectric charge; and paired electrodes configured to change a movementdirection of the charged droplet.
 4. The flow cytometer system accordingto claim 1, wherein the processor circuitry is configured to calculatethe fluorescence intensity by approximating measured spectra based onthe linear sum of the single-dyeing spectra.
 5. The flow cytometersystem according to claim 3, wherein the approximation of the measuredspectra based on the linear sum of the single-dyeing spectra is carriedout by using a least-squares method.
 6. The flow cytometer systemaccording to claim 3, wherein the approximation of the measured spectrabased on the linear sum of the single-dyeing spectra is carried out byusing a linear least-squares method.
 7. The flow cytometer systemaccording to claim 3, wherein the approximation of the measured spectrabased on the linear sum of the single-dyeing spectra is carried out byusing a weighted least-squares method.
 8. The flow cytometer systemaccording to claim 1, wherein the plot diagram represents the calculatedfluorescence intensity of two different fluorescence dyes.
 9. The flowcytometer system according to claim 1, wherein the processor circuitryis configured to output a plurality of dot diagrams representing thecalculated fluorescence intensity of different fluorescent dyes for eachrespective fluorescent dye.
 10. The flow cytometer system according toclaim 1, wherein the microparticles are cells.
 11. The flow cytometersystem according to claim 1, wherein the microparticles are syntheticparticles.
 12. The flow cytometer system according to claim 1, whereinthe number of the fluorescent dyes is more than five.
 13. The flowcytometer system according to claim 12, wherein the number of thefluorescent dyes is more than twelve.
 14. The flow cytometer systemaccording to claim 1, wherein the fluorescent dyes include at least oneof FITC, PE, PerCP, PerCP-Cy5.5, PE-Cy7, APC, APC-Cy7, AF488, PE, PI,Alexa500, Alexa514, Alexa532, PE-TR, PI, Alexa600, or PE-Cy5.
 15. Theflow cytometer system according to claim 14, wherein the fluorescentdyes include PE, PE-Cy7, PE-Cy5, and APC.
 16. The flow cytometer systemaccording to claim 1, further comprising a plurality of laser lightsources configured to radiate laser beams through a flow cell where themicroparticles flow.
 17. The flow cytometer system according to claim16, wherein the laser light sources include at least one of a 488 nmlaser or a 640 nm laser.
 18. The flow cytometer system according toclaim 17, wherein the detectors include first detectors configured toreceive the light excited by the 488 nm laser and second detectorsconfigured to receive the light excited by the 640 nm laser.
 19. Theflow cytometer system according to claim 1, wherein the detectors areconfigured to receive a light from each of microparticles labeled with asingle fluorescent dye of the fluorescent dyes, and wherein theprocessor circuitry is configured to store single-dyeing spectraobtained by the detectors.
 20. The flow cytometer system according toclaim 1, wherein the processor circuitry is configured to read outsingle-dyeing spectra that was previously stored.
 21. The flow cytometrysystem according to claim 1, wherein the processor circuitry isconfigured to read out single-dyeing spectra obtained by preparingmicroparticles labeled with a single fluorescent dye from measuredspectra obtained by the detectors.
 22. A method comprising: receiving,by a plurality of detectors, a light from each of microparticles labeledwith a plurality of fluorescent dyes, and the detectors corresponding todifferent received light wavelength bands; calculating, by a processor,fluorescence intensity for each of the fluorescent dyes using a linearsum of single-dyeing spectra, wherein a number of single-dyeing spectrabeing equal or less than a number of the detectors; and outputting, bythe processor, a plot diagram of the calculated fluorescence intensity.23. The method according to claim 22, further comprising: vibratingsample liquid including the microparticles; charging a droplet generatedby the vibrating element with electric charge; and changing a movementdirection of the charged droplet.
 24. The method according to claim 22,further comprising: calculating the fluorescence intensity byapproximating measured spectra based on the linear sum of thesingle-dyeing spectra.
 25. The method according to claim 24, wherein theapproximation of the measured spectra based on the linear sum of thesingle-dyeing spectra is carried out by using a least-squares method.26. The method according to claim 24, wherein the approximation of themeasured spectra based on the linear sum of the single-dyeing spectra iscarried out by using a linear least-squares method.
 27. The methodaccording to claim 24, wherein the approximation of the measured spectrabased on the linear sum of the single-dyeing spectra is carried out byusing a weighted least-squares method.
 28. The method according to claim22, wherein the number of the fluorescent dyes is more than twelve. 29.The flow cytometer system according to claim 1, wherein the plot diagramrepresents the calculated fluorescence intensity of two differentfluorescence dyes.
 30. A non-transitory computer readable medium storinga program, which when executed by at least one processor, is configuredto execute to cause: receiving, by a plurality of detectors, a lightfrom each of microparticles labeled with a plurality of fluorescentdyes, and the detectors corresponding to different received lightwavelength bands; and calculating, by the at least one processor,fluorescence intensity for each of the fluorescent dyes using a linearsum of single-dyeing spectra.